Deviant logic and the paradoxes of self reference

The paradoxes of self reference have to be dealt with by anyone seeking to give a satisfactory account of the logic of truth, of properties, and even of sets of numbers. Unfortunately, there is no widespread agreement as to how to deal with these paradoxes. Some approaches block the paradoxical inferences by rejecting as invalid a move that classical logic counts as valid. In the recent literature, this deviant logic analysis of the paradoxes has been called into question.This disagreement motivates a re-examination of the philosophy of formal logic and the status of logical truths and rules. In this paper I do some of this work, and I show that this gives us the means to defend the deviant approaches against such criticisms. As a result I hope to show that these analyses of the paradoxes are worthy of more serious consideration than they have so far received.Letting a hundred flowers blossom and a hundred schools of thought contend is the policy for promoting the progress of the arts and the sciences.— Mao Tse-TungDedicated to Bob Meyer on the occasion of his 60th BirthdayThis paper was presented to the Department of Philosophy of the University of Queensland, and the 1992 Australasian Association of Philosophy Conference. I'm grateful for comments and criticism from those present; especially Graham Priest, Gary Malinas, Ian Hinckfuss, Mark Lance and Lloyd Reinhardt. The paper has a second half Comparing Deviant Logics that was read at the 1992 Australasian Association for Logic Conference, held in honour of Bob Meyer. Both are dedicated to him with appreciation for his work which, as many can see, provides inspiration for this conception of logic.